Ultrahigh-Resolution Microwave Spectroscopy on TrappedYb+171Ions

Precision Physics in Penning Traps Using the Continuous Stern-Gerlach Effect

Abstract“A single atomic particle forever floating at rest in free space” (H. Dehmelt) would be the ideal object for precision measurements of atomic properties and for tests of fundamental theories. Such an ideal, of course, can ultimately never be achieved. A very close approximation to this ideal is made possible by ion traps, where electromagnetic forces are used to confine charged particles under well-controlled conditions for practically unlimited time. Concurrently, sensitive detection methods have been developed to allow observation of single stored ions. Various cooling methods can be employed to bring the trapped ion nearly to rest. Among different realisations of ion traps we con…

Spectroscopy of excited state positronium

Electric dipole transitions in the microwave range have been induced between the fine-structure levels of positronium in the excited staten=2. As an indication of the transitions, we used the increase in Lyman-α radiation when the metastable 23S1-level is depopulated. The results for the transitions 23S1→23P0,1,2 areΝ 0=18499.65±1.20±4.00 MHz,Ν 1=13012.42 ±0.65±1.54 MHz andΝ 2=8624.38±0.54±1.40 MHz. The first error is statistical and the second systematic. The precision of the present measurement has improved by a factor of 3, compared to previous data. Recent bound state QED-calculations have been extended to the orderR t8 α 4lnα −1. The not yet completely calculated orderR t8 α 4 is estim…

Possible Precision Far—Infrared Spectroscopy on Trapped Ions

One of the necessary conditions for very high resolution spectroscopy is the existence of long-living energy levels between which transitions can be induced by tunable electromagnetic radiation. Moreover the observation time of the particles under investigation should be sufficiently long, and perturbing effects like Doppler broadening and collisions should be very small. All this leads to the technique of trapped ion spectroscopy which offers all the required conditions. It uses the confinement of charged particles to a very small volume in space under ultrahigh vacuum conditions either by application of a r.f. voltage and a small additional d.c. bias to an arrangement of three electrodes …

A Three Dimensional Lattice of Ion Traps

We propose an ion trap configuration such that individual traps can be stacked together in a three dimensional simple cubic arrangement. The isolated trap as well as the extended array of ion traps are characterized for different locations in the lattice, illustrating the robustness of the lattice of traps concept. Ease in the addressing of ions at each lattice site, individually or simultaneously, makes this system naturally suitable for a number of experiments. Application of this trap to precision spectroscopy, quantum information processing and the study of few particle interacting system are discussed.

Hyperfine-structure measurements on trapped Pb II.

The 6${\mathit{P}}_{3/2}$-6${\mathit{P}}_{1/2}$ magnetic dipole resonance transition in ${\mathrm{Pb}}^{+}$ has been observed by cw laser excitation of an ion cloud stored in a Paul trap and subsequent detection of the fluorescence radiation. From the hyperfine-structure splitting of the spectrum we determine the A factor for the ground state, A(${\mathit{P}}_{1/2}$)=12.967(13) GHz, and the excited state, A(${\mathit{P}}_{3/2}$)=0.580(3) GHz. From a contamination of $^{208}\mathrm{Pb}$ in our sample we derived the $^{207}\mathrm{Pb}^{+}$${\mathrm{\ensuremath{-}}}^{208}$${\mathrm{Pb}}^{+}$ isotope shift [\ensuremath{\Delta}\ensuremath{\nu}=311(14) MHz]. A small electric quadrupole admixture …

Fabrication of a planar micro Penning trap and numerical investigations of versatile ion positioning protocols

We describe a versatile planar Penning trap structure, which allows one to dynamically modify the trapping configuration almost arbitrarily. The trap consists of 37 hexagonal electrodes, each with a circumcircle diameter of 300 μm, fabricated in a gold-on-sapphire lithographic technique. Every hexagon can be addressed individually, thus shaping the electric potential. The fabrication of such a device with clean room methods is demonstrated. We illustrate the variability of the device by a detailed numerical simulation of a lateral and a vertical transport and simulate trapping in racetrack and artificial crystal configurations. The trap may be used for ions or electrons, as a versatile cont…

A simple method for counting the number of trapped ions in an ion trap

The number of stored Ca\(^+\) ions in an ion trap was measured optically by utilizing the metastable states. All the ions trapped are first pumped into the metastable \(D\) states. The ions in the metastable \(D\) states are transferred to the ground \(S\) state via the \(P\) state by exciting a \(D\rightarrow P\) transition. Each ion then emits one photon through a subsequent \(P\rightarrow S\) spontaneous emission. Thus, the number of photons is the same as the number of trapped ions initially in the metastable states. When a fraction of all the stored ions are pumped into the metastable states, the method is still applicable if the fraction of the ions is known.

Lifetime measurements of the 3D3/2 and 3D5/2 metastable states in CaII

The lifetime of the metastable 3D3/2 and 3D5/2 states of Ca+ ions is determined in a r.f. ion trap by laser excitation of this levels and subsequent time delayed probing of the state population by a second laser. In a buffer gas atmosphere of about 10−5−10−6 mbar of He we observe quenching to the ground state and strong finestructure mixing of the two D-states. This mixing allowes only the determination of the combined lifetime. Our result of τ(3D)=1.24(39) s is in good agreement with theoretical calculations.

The g Factor of Hydrogenic Ions: A Test of Bound State QED

We present a new experimental value for the magnetic moment of the electron bound in hydrogenlike carbon (12C5+): g exp = 2.001 041 596 (5). The experiment was carried out on a single 12C5+ ion stored in a Penning trap. The high accuracy was made possible by spatially separating the induction of spin flips and the analysis of the spin direction. Experiment and theory test the bound-state QED contributions to the gJ factor of a bound electron to a precision of 1%. We discuss also implications of the experiment on the knowledge of the electron mass.

Vibrational population of H 2 + after electroionization of thermal H2

In an ion trap experiment we have determined the vibrational population of the lowest 9 vibrational levels of H2+. We used photodissociation of the trapped molecules by 248 nm light from an excimer laser and the dependence of the photodissociation cross section from the vibrational state. Our results are in good agreement to calculations, which are based on the Franck-Condon principle, but include a variation of the internuclear distance in the transition matrix element.

Determination of the g-Factor of Single Hydrogen-Like Ions by Mode Coupling in a Penning Trap

A method has been developed and applied for the determination of the electronic g-factor of single hydrogen-like ions stored in a Penning trap. The method is based on mode coupling of the ion trapping motions and is conceptionally advantageous as compared to previously used methods. It has been applied to hydrogen-like oxygen 16O7+ and yields a value for the gJ-factor which is in agreement with previously determined values. Experimental requirements and possibilities of the new method are discussed.

Antihydrogen production in a combined trap

In this paper we study the properties of a Paul trap with a superimposed magnetic field (combined trap) and discuss the possibility of using this trap to simultaneously store positrons and antiprotons to form antihydrogen.

Precise lifetime determination of the metastable 3d 2 D 5/2 level in Ca + by "electron shelving"

Ca+ ions confined as a cloud in a Paul trap were excited and cooled by radiation from two lasers, tuned to the 4s2S1/2 − 4p2P1/2 and 4p2P1/2 − 3d2D3/2 transitions. The strong fluorescence of these lines disappears when we excite the ions simultaneously by a third laser on the 3d2D3/2 − 4p2P3/2 line because of population trapping in the metastable 3d2D5/2 state, into which the 4p2P3/2 level decays. From the time dependence of the fluorescence after blocking the third laser we determined the lifetime of the 3d2D5/2 level. Our result of τ = 1064(17) ms improves earlier results and agrees with the value recently computed by Liaw using the Brueckner approximation.

Fractional frequency collective parametric resonances of an ion cloud in a Paul trap

ion cloud ina Paul trap driven at simple fractions of twice the secular frequency of the trap by an additionally appliedquadrupole field. The fractional resonances are observable only if the excitation field surpasses a criticalstrength. Odd-even staggering of the thresholds is observed.@S1050-2947~98!51307-8#PACS number~s!: 32.80.Pj, 07.75.1h

On the possible determination of hyperfine anomalies by trapped ion spectroscopy

Abstract Laser-microwave double-resonance techniques in radiofrequency (rf) traps and Penning traps represent a powerful tool to determine hyperfine structure splittings as well as nuclear g factors to high precision. While hyperfine structure constants have been determined in a number of cases below the 10 −10 level of precision, electronic g factors have been measured to 10 −7 and there are good prospects of obtaining similar accuracy for g l . Moreover sensitive techniques have been developed for injection of ions from outside the trap. This opens the possibility to determine hyperfine anomalies at least to the 1% level of precision for chains of unstable isotopes.

Spatial separation of atomic states in a laser-cooled ion crystal

A laser cooled ion crystal containing several hundred Ca+ ions has been stored in a linear Paul trap. Cooling is provided by a red detund laser at the 4S1/2−4P1/2 resonance transition. A second laser serves for repumping of those ions which decay from the excited 4P1/2 level to the metastable 3D3/2 state. The ions can be additionally excited by a third laser to a long lived metastable 3D5/2 energy level which decouples them from the cooling laser radiation. The light pressure acting upon the laser cooled ions pushes them into the direction of the laser beam. The ions in the metastable 3D5/2 state, however, do not experience any light pressure force and diffuse to the crystal side which poin…

Hyperfine structure measurements in the

Clouds of stable and unstable Eu+ isotopes have been confined in a Paul trap, each containing about 105 particles. In a microwave-optical double resonance experiment several hyperfine separations in the 4f7 6s 7S3 exited level have been measured with the experimental uncertainties ranging between 10-8 and 3×10-6. These experiments have confirmed that also in the case of an excited level with a large number of hyperfine or Zeeman sublevels the microwave-optical double resonance technique in a Paul trap can be useful for precise hyperfine structure investigation. The hyperfine coupling constants A and B have been determined for the isotopes 153Eu+, 151Eu+, 150Eu+ and 148Eu+. The results compl…

Subharmonic excitation of the eigenmodes of charged particles in a Penning trap

When parametrically excited, a harmonic system reveals a nonlinear dynamical behaviour which is common to non-deterministic phenomena. The ion motion in a Penning trap -- which can be regarded as a system of harmonic oscillators -- offers the possibility to study anharmonic characteristics when perturbed by an external periodical driving force. In our experiment we excited an electron cloud stored in a Penning trap by applying an additional quadrupole r.f. field to the endcaps. We observed phenomena such as individual and center-of-mass oscillations of an electron cloud and fractional frequencies, so-called subharmonics, to the axial oscillation. The latter show a characteristic threshold b…

Theg-factor of highly charged ions

Highly charged ions provide a unique opportunity to test our understanding of atomic properties under extreme conditions: The electric field strength seen by an electron bound to a nucleus at the distance of the Bohr radius ranges from 1010 V/cm in hydrogen to1016 V/cm in hydrogenlike uranium. The theory of quantum electrodynamics (QED) allows for calculation e.g. of binding energies, transition probabilities or magnetic moments. While at low fields QED is tested to very high precision, new, hypothetical nonlinear effects like photon- photon interaction or a violation of Lorentz symmetry may occur in strong fields which then would lead to an extension of the Standard Model. The ultra-high p…

The magnetic moment anomaly of the electron bound in hydrogen-like oxygen16O7 

The measurement of the g-factor of the electron bound in a hydrogen-like ion is a high-accuracy test of the theory of quantum electrodynamics (QED) in strong fields. Here we report on the measurement of the g-factor of the bound electron in hydrogen-like oxygen (16O7+). In our experiment a single highly charged ion is stored in a Penning trap. The electronic spin state of the ion is monitored via the continuous Stern?Gerlach effect in a quantum non-demolition measurement. Quantum jumps between the two spin states (spin up and spin down) are induced by a microwave field at the spin precession frequency of the bound electron. The g-factor of the bound electron is obtained by varying the micro…

Phase-sensitive measurement of trapped particle motions

We have developed and applied a novel method for the precise determination of small frequency differences of particle motions inside a Penning trap. In the present case, the frequency differences on the order of 100 mHz at motional frequencies on the order of 1 MHz are used to determine the spin state of an electron bound in a hydrogen-like ion. This novel technique measures the integrated phase difference of the particles' motions relative to an excitation with a well-defined phase. Thereby, the Fourier-limit for frequency measurements based on Fourier-analyses of detection signals can be overcome.

Ground-state hyperfine-structure measurements of unstableEu+isotopes in a Paul ion trap

Hyperfine separations in unstable ${\mathrm{Eu}}^{+}$ ions of mass 148, 149, and 150 have been measured in laser-microwave double-resonance experiments in a Paul ion trap. In spite of the small available quantities of the isotopes, the experimental uncertainties are of the order of ${10}^{\ensuremath{-}8}$ or below, which is of the same order as in earlier measurements on stable isotopes of ${\mathrm{Eu}}^{+}.$ Extensive second-order perturbation calculation is required to obtain coupling constants for magnetic-dipole $(A)$ and electric-quadrupole $(B)$ interactions. The uncertainties are a few times ${10}^{\ensuremath{-}7}$ for $A$ and ${10}^{\ensuremath{-}3}$ for $B.$ The experiments are …

Lifetime of the metastable 6P 3/2 level of PbII

Pb+-ions were stored in a r.f.-quadrupole trap. Short laser pulses at a 710-nm M1-transition excited the ions to the metastable 6P 3/2 level. Time-resolved registration of the subsequent decay photons at the same wavelength directly gives the lifetime of that state. No dependence of the decay rate on the density of different buffer gases up to 10−5 mbar pressure was observed and from this we deduced upper limits to the quenching cross section. We have observed, however, a small dependence on the stored ion number. The final result for the lifetime is 41.2 ± 0.7 ms in agreement with the result of a previous calculation.

Highly charged ions, quantum-electrodynamics, and the electron mass

Abstract High precision experiments on the magnetic moment of hydrogen-like ions confined in a Penning trap have provided the most stringent test of bound-state quantum-electrodynamic calculations. Experiments have been performed on single C 5+ and O 7+ ions. These experiments are briefly reviewed and prospects for future improvements and extension to other systems are discussed.

Instabilities of ion motion in a linear Paul trap

Abstract We have investigated the stability properties of a linear radio frequency ion trap with cylindrical electrodes. Inside the region of stability for an ideal trap we found a number of instabilities similar to those experimentally observed in three-dimensional traps. They arise from higher order contributions to the ideal quadrupole trapping potential. The static potential for axial confinement shifts the radial ion oscillation frequencies and leads to additional instabilities.

Axialisation, cooling and quenching of $\mathsf{Ba^+}$ ions in a Penning trap

Collisions of ions, stored in a Penning trap, with neutral background molecules usually lead to rapid ion loss from the trap unless the ions are excited by the sum of the frequencies of the reduced cyclotron and magnetron motion. Then the ions are cooled by collisions and are driven to the trap centre leading to substantial increase of the storage time. Furthermore in a three level system including a long living metastable state collisions deexcite this metastable state and increase the population density in the ionic ground state. In a laser spectroscopic experiment we demonstrate the advantages of collisions on Ba+ ions stored in a Penning trap. The combined action of metastable state que…

Würfelt Gott doch?

Albert Einstein konnte sich nie mit den Zumutungen der Quantenmechanik anfreunden. Eines der Phanomene, die ihm merkwurdig erschienen, ist die „Verschrankung“, nach der in bestimmten Fallen die Eigenschaften zweier Teilchen nur gemeinsam bestimmt sind. Eine Messung einer Eigenschaft an einem Teilchen legt demnach auch die des anderen fest – auch wenn die Entfernung zwischen ihnen eine Wechselwirkung und damit eine ursachliche Einflussnahme ausschliest. In einem Brief an Max Born schrieb Einstein 1926: „Die Quantenmechanik … liefert viel, aber dem Geheimnis des Alten bringt sie uns kaum naher. Jedenfalls bin ich uberzeugt, dass der nicht wurfelt.“ Nach seiner Ansicht mussen in jeder Theorie …

Individual and center-of-mass resonances in the motional spectrum of an electron cloud in a Penning trap

We have examined experimentally the motional spectrum of an electron cloud confined in a Penning trap. When the axial oscillation is excited by a radio frequency field the resonance exhibits a double structure. Both components depend differently on the number of trapped electrons and have different shape and width. We conclude that one of them corresponds to the excitation of the individual electrons while the other is the center-of-mass mode of the cloud. The threshold behaviour of the center-of-mass resonance suggests that it is a parametric instability of a Mathieu type equation of motion.

3d

We have measured the lifetime of the metastable 3D 5/2 level in Ca+ using the “quantum jump" technique on a single stored and laser cooled ion in a linear Paul trap. We found a linear dependence of the measured decay rate on the power of the laser which repumps the ions from the long lived 3D 3/2 level. This can be explained by off-resonant depletion of the 3D 5/2 level. The proper lifetime of this level is obtained by a linear extrapolation of the measured lifetime to zero laser power. We obtain 1100(18) ms in agreement with theoretical calculations. The observed systematic change of the decay rate resolves discrepancies between earlier experiments in which this effect had not been conside…

g Factor of Lithiumlike Silicon: New Challenge to Bound-State QED

The recently established agreement between experiment and theory for the $g$ factors of lithiumlike silicon and calcium ions manifests the most stringent test of the many-electron bound-state quantum electrodynamics (QED) effects in the presence of a magnetic field. In this Letter, we present a significant simultaneous improvement of both theoretical $g_\text{th} = 2.000\,889\,894\,4\,(34)$ and experimental $g_\text{exp} = 2.000\,889\,888\,45\,(14)$ values of the $g$ factor of lithiumlike silicon $^{28}$Si$^{11+}$. The theoretical precision now is limited by the many-electron two-loop contributions of the bound-state QED. The experimental value is accurate enough to test these contributions…

Instabilities of an electron cloud in a Penning trap

We have measured the storage instabilities of electrons in a Penning trap at low magnetic fields. These measurements are carried out as a function of the trapping voltage, for different magnetic fields. It is seen that these instabilities occur at the same positions when the trapping voltage is expressed as a percentage of the maximum voltage, given by the stability limit. The characteristic frequencies at which these instabilities occur, obey a relation that is given by n zω z + n +ω + + n -ω - = 0, where ω z, ω + and ω - are the axial, perturbed cyclotron and the magnetron frequencies of the trapped electrons respectively, and the n's are integers. The reason for these instabilities are a…

Collisional relaxation measurements on Pb+ hyperfine levels

The time constants for population relaxation of optically pumped Pb+ ions in a Paul ion trap have been determined in a He buffer gas atmosphere with additional components of other gases. For the 6P1/2 ground state of Pb+ and an ion temperatur of 104 K we find cross sections of 0.72(0.33)·10−17 cm2; 0.59(0.38)·10−15 cm2; and 2.56(0.74)·10−14 cm2 for He, N2 and O2, respectively. The error includes an estimated 20% uncertaincy in the pressure calibration of a residual gas analyser.

Nonlinear collective oscillations of an ion cloud in a Paul trap

In an experiment using a Paul trap, we create a ${\mathrm{H}}_{2}^{+}$ ion cloud by electron ionization of the background gas at ${10}^{\ensuremath{-}9}$-mbar residual pressure. Exciting the ions parametrically at twice the frequency of the secular motion of ions in the $r$ or $z$ direction, we observe a narrow resonance at some distance from the motional resonance center if the amplitude of the exciting field exceeds a threshold value. The threshold value decreases with increasing ion number. Since the narrow resonance does not shift with ion number, we interpret it as a collective resonance of the center of mass of the ion cloud. The resonance shape exhibits the typical form of a driven a…

Adiabatic cooling of antiprotons in a Penning trap

An antiproton cloud cooled at 4.2 K in a Penning trap can be further cooled by adiabatic reduction of the trap magnetic and electric fields. It will be shown that the temperature can be reduced by two orders of magnitude. This cooling method may be useful to obtain ultra-low energy antiprotons for the measurement of their gravitational properties and the production of ultra-low energy antihydrogen atoms.

The $\mathsf{g_{\scriptscriptstyle J}}$ -factor in the ground state of Ca $^\mathsf{+}$

We have determined the $g_{\scriptscriptstyle J}$ -factor of the Ca + ion in the electronic 4S1/2 ground state on a cloud of ions confined in a Penning trap with a superimposed magnetic field of 1.43 T. We use a c.w. laser to prepare a Zeeman substate by optical pumping and induce $\Delta m_J=1$ transitions by a resonant microwave field at 40 GHz. Resonance is detected by a change in the fluorescence intensity originating from the ion cloud. We obtain a full width in the resonance of a few kHz and the fractional uncertainty of the line center, taking the average of several measurements, was 4 x 10-8. After calibrating the magnetic field by the cyclotron frequency of electrons stored in the …

Hyperfine structure andg-factor measurements in ion traps

We report about measurements on ground-state hyperfine splitting constants of stable Eu+ isotopes in radio frequency ion traps and experiments on the electronicg-factor of Ba+ in a Penning trap. From the precision of both measurements, which ranges between 3·10−6 and 5·10−7, we conclude that precise determination of the differential Bohr-Weisskopf effect in chains of isotopes will be possible in the near future.

Measurement of the ground state hyperfine splitting in207Pb II

The ground state hyperfine splitting of simply ionized lead has been determined using pulsed laser excitation of electrodynamically confined ions. We obtain ΔV(6P1/2)=12.85(10) GHz

g-factor measurement of hydrogenlike28Si13+as a challenge to QED calculations

Using a phase-detection method to determine the cyclotron frequency of a single trapped ion in a Penning trap allowed us to perform a measurement of the $g$ factor of the bound electron in hydrogenlike ${}^{28}$Si${}^{13+}$ with a statistical uncertainty of $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$. Furthermore, we reevaluated the image-charge shift as the main source of uncertainty. Our result challenges bound-state quantum-electrodynamical calculations by probing two-loop contributions of order (Z$\ensuremath{\alpha}$)${}^{6}$ and paves the way towards a more precise determination of fundamental constants as the electron mass.

Electrong-factor determinations in Penning traps

The magnetic moment of the electron, expressed by the g-factor in units of the Bohr magneton, is a key quantity in the theory of quantum electrodynamics (QED). Experiments using single particles confined in Penning traps have provided very precise values of the g-factor for the free electron as well as the electron bound in hydrogen-like ions. In this paper the status of these experiments is reviewed. The results allow testing calculations of higher order Feynman diagrams. Comparison of experimental and theoretical results for free and bound particles show no discrepancy within the limits of error, thus representing to date the most sensitive test of QED. Moreover, the g-factor provides a u…

Improved lifetime measurements of the 3D3/2 and 3D5/2 metastable states of Ca II

The lifetimes of both metastable 3D-levels of Ca+ have been measured using the ion storage technique. Operation at UHV-conditions eliminated the earlier reported problems of collisional finestructure mixing between those states [1], which is inherent to measurements at buffergas background. The results of τ(D 3/2)=1113(45) ms and τ(D 5/2)=1054(61) ms improve our earlier result [1] by almost one order of magnitude and are in good agreement with recent theoretical calculations [3, 4, 5].

Observation of instabilities in a Paul trap with higher-order anharmonicities

Systematic measurements of the relative ion number stored in a Paul trap within the stability diagram given by the solution of the equation of motion reveal many lines, where only few or no ions can be confined. The observations can be explained by the presence of perturbations from higher-order components in the trapping potential, which is a quadrupole potential in the ideal case. The resonances follow the equation (nr/2)βr + (nr/2)βz = 1,nr +nz =N, where 2N is the order of the perturbation,nr,nz are integer andβr,βz are stability parameters of the trap. The experiments were performed on H+ and H2+ ions, which are detected after a storage time of 0.3 s by ejection from the trap.

Ion trap nuclear resonance on $\mathsf{^{151}Eu^ + }$

Laser-microwave double resonance techniques applied to a cloud of a natural mixture of Eu + isotopes confined in a Penning trap has been used to induce and detect nuclear Zeeman transitions. In spite of the complex level structure of Eu + and overlapping spectra from the two isotopes five different $\Delta m_I = 1$ transitions could be observed from which the nuclear magnetic moment can be derived. We obtain for 151 Eu + g I = 1.377 34(6) demonstrating the potential for high accuracy of the technique. The experiment can be considered as a feasibility test that precise spectroscopy data using the ion storage technique can be obtained of very complex ions and under unfavourable conditions.

A Possible New Value for the Electron Mass from g-Factor Measurements on Hydrogen-Like Ions

The mass of the electron in atomic units (m e) represents the largest error contribution in an experiment to determine the g-factor of the electron bound in hydrogen-like carbon. Recent progress in the calculation reduces the uncertainty of the theoretical value to such a low value that m e can be determined from a comparison of experimental and theoretical g-factors. The present preliminary value of the electron mass agrees with the accepted value but reduces the uncertainty by about a factor 2.

Lifetime of the 4D 3/2 and 4D 5/2 metastable states in Sr II

Sr+ ions were confined in a r.f. quadrupole trap for times of the order of 30 min. The metastable 4D states were populated via laser excitation of the 5P states. The weak quadrupole transition rate into the 5S 1/2 ground state at 674 and 687 nm was deduced from observation of the exponential decay. At background pressures above 10−7 mbar the radiative decay is dominated by collisional quenching. Extrapolation of the observed decay rate to zero background pressure yields the radiative lifetimes. At pressures around 10−6 mbar fine structure mixing collisions between the 4D states have been observed, which lead to corrections of the extrapolated lifetimes. As the final result we obtain 395±38 …

Experimental ground stateg J-factor of Ba+ in a Penning ion trap

We observed the Zeeman-splitting of the 6S1/2 – 6P1/2 resonance transition of Ba+-ions (493.4 nm) in a 6T magnetic field. The ions were stored in a Penning quadrupole trap. We polarized the ground state by optical pumping and in a microwave-optical double resonance experiment we measured the ground state Zeeman-splitting. From the resonance frequency and the cyclotron frequency of electrons stored in the same trap we derived theg-factor of the 6S1/2 state. The result isgJ(6S1/2)=2.002 490 6(11), in reasonable agreement with recent calculations.

Quasienergy states of trapped ions

The quantum models for a single trapped ion are extended to the description of the collective dynamics for systems of ions confined in quadrupole electromagnetic traps with cylindrical symmetry. A class of quantum Hamiltonians with suitable axial and radial interaction potentials given by homogeneous functions of degree (-2) and invariant under translations and axial rotations are introduced. The considered axial and radial quantum Hamiltonians for the center-of-mass and relative motions are described by collective dynamical systems associated to the symplectic group \(\). Discrete quasienergy spectra are obtained and the corresponding quasienergy states are explicitly realized as \(\) cohe…

Continuous Stern–Gerlach effect and the magnetic moment of the antiproton

Abstract The measurement of the magnetic moment (or g-factor ) of the antiproton and of the proton is a sensitive test of CPT invariance. We discuss the possibility of applying the continuous Stern–Gerlach effect to detect quantum jumps between the two spin states (spin up and spin down) of the antiproton. The measurement will be performed on a single antiproton stored in a Penning trap. The g -factor of the antiproton is determined by measuring its cyclotron frequency and its spin precession frequency in the magnetic field of the trap. With the double Penning trap method the g -factor of the antiproton can be determined with an accuracy of 1 ppb.

Shifts of the 3D - 4P transitions in different isotopes of positive calcium ions

A sample of stable isotopes containing the masses 40, 42, 43 and 44 was stored under buffer-gas conditions in a Paul ion trap. After population of the metastable 3D levels by spontaneous decay of the laser-excited 4P state we observed laser-induced fluorescence when we scanned a laser across the different 3D - 4P fine-structure lines at 850, 854 and 866 nm. From the Doppler-limited lines of these transitions we deduced the isotope shifts, which are of the order of several GHz due to the large specific mass shift of the metastable 3D levels.

Experimental and theoretical challenges for the trapped electron quantum computer

We discuss quantum information processing with trapped electrons. After recalling the operation principle of planar Penning traps we sketch the experimental conditions to load, cool and detect single electrons. Here we present a detailed investigation of a scalable scheme including feasibility studies and the analysis of all important elements, relevant for the experimental stage. On the theoretical side, we discuss different methods to couple electron qubits. We estimate the relevant qubit coherence times and draw implications for the experimental setting. A critical assessment of quantum information processing with trapped electrons is concluding the article.

Spatial separation of atomic states in a laser cooled ion crystal

A laser cooled ion crystal containing several hundred Ca+ ions has been stored in a linear Paul trap. Cooling is provided by a red detund laser at the 4S1/2−4P1/2 resonance transition. A second laser serves for repumping of those ions which decay from the excited 4P1/2 level to the metastable 3D3/2 state. The ions can be additionally excited by a third laser to a long lived metastable 3D5/2 energy level which decouples them from the cooling laser radiation. The light pressure acting upon the laser cooled ions pushes them into the direction of the laser beam. The ions in the metastable 3D5/2 state, however, do not experience any light pressure force and diffuse to the crystal side which poin…

High-Precision Measurements of the Bound Electron’s Magnetic Moment

Highly charged ions represent environments that allow to study precisely one or more bound electrons subjected to unsurpassed electromagnetic fields. Under such conditions, the magnetic moment (g-factor) of a bound electron changes significantly, to a large extent due to contributions from quantum electrodynamics. We present three Penning-trap experiments, which allow to measure magnetic moments with ppb precision and better, serving as stringent tests of corresponding calculations, and also yielding access to fundamental quantities like the fine structure constant α and the atomic mass of the electron. Additionally, the bound electrons can be used as sensitive probes for properties of the …

Influence of anharmonicities of a Paul trap potential on the motion of stored ions

Ground- and excited stateg-factors of Ba+

We observed the Zeeman-splitting of the 6S 1/2-6P 1/2 resonance transition of Ba+ ions (493.4 nm) in a 6 T magnetic field. The ions were stored in a Penning quadrupole trap. From the splitting and the simultaneously measured cyclotron frequency of stored electrons we derived theg-factors of the 6S 1/2 and 6P 1/2 states. The results areg(6S 1/2)=2.00267(20) andg(6P 1/2)=0.66634(22).

Determination of the helium-4 mass in a Penning trap

We have measured the cyclotron frequencies of He+, H+ 2 and D+ 2 ions in a room temperature Penning trap. The resonances were detected destructively by a time-of-flight technique. The statistical uncertainty of the resonance frequencies was generally below 1 ppb. A detailed account of measures to minimize systematic frequency shift is presented. Using the accepted values for the proton and deuteron mass we obtain a value for the 4He mass: M(4 He) = 4.0026032489(22) (0.5 ppb). It is in agreement with the accepted value.

Electron and positron cooling of highly charged ions in a cooler Penning trap

Abstract Electron cooling is a well-established technique to increase the phase space density of particle beams in storage rings. In this paper, we discuss the feasibility of electron and positron cooling of ions in a Penning trap. We calculate the cooling times for the cases of trapped bare ions with nuclear charge Z =1 (protons), Z =36 (krypton) and Z =92 (uranium) with the Spitzer formula. Our calculations show that for typical experimental conditions the time for cooling from initial energies of 10 keV per charge down to rest is in the order of a second. We investigate the dependence of the cooling time on the number of ions and electrons, and their charge and mass.

Measurement of the electronicgfactor ofH2+

Ion trapping and spin-dependent charge-exchange techniques were used to determine the electron g factor of ${\mathrm{H}}_{2}^{+}$ as a first step to provide a precise test of the theory of molecular g factors. Accessible to us were the vibrational states 4, 5, and 6. Averaged over these vibrational states we obtain g(v=4,5,6) =2.002 2837(18) 7(18) in agreement with the corresponding theoretical value of g=2.002 282 8(8). As a by-product we have measured the rotational g factor to be ${g}_{\mathrm{rot}=0.920(40)}$, compared with the calculated value of ${g}_{\mathrm{rot}=0.9244}$.

Isotope dependence of the Zeeman effect in lithium-like calcium

The magnetic moment μ of a bound electron, generally expressed by the g-factor μ=−g μB s ħ−1 with μB the Bohr magneton and s the electron's spin, can be calculated by bound-state quantum electrodynamics (BS-QED) to very high precision. The recent ultra-precise experiment on hydrogen-like silicon determined this value to eleven significant digits, and thus allowed to rigorously probe the validity of BS-QED. Yet, the investigation of one of the most interesting contribution to the g-factor, the relativistic interaction between electron and nucleus, is limited by our knowledge of BS-QED effects. By comparing the g-factors of two isotopes, it is possible to cancel most of these contributions an…

Hyperfine structure andg-factor measurements in ion traps

We report about measurements on ground-state hyperfine splitting constants of stable Eu+ isotopes in radio frequency ion traps and experiments on the electronicg-factor of Ba+ in a Penning trap. From the precision of both measurements, which ranges between 3·10−6 and 5·10−7, we conclude that precise determination of the differential Bohr-Weisskopf effect in chains of isotopes will be possible in the near future.

ExperimentalgJfactor in the metastable 5D3/2level ofBa+

The Zeeman splitting of the metastable 5${\mathit{D}}_{3/2}$ level of $^{138}\mathrm{Ba}^{+}$ in a magnetic field of 6 T has been measured in a laser-microwave double resonance experiment in a Penning ion trap. The magnetic field at the ion's position is determined by the cyclotron frequency of electrons stored in the same trap. From the ratio of both transition frequencies we obtain a ${\mathit{g}}_{\mathit{J}}$ value of 0.799 327 8(3). As a by-product, we confirmed earlier measurements on the 6${\mathit{S}}_{1/2}$ ground-state ${\mathit{g}}_{\mathit{J}}$ factor to 2.002 492 2(10). The precision in both experiments is sufficient to test relativistic many-body calculations. \textcopyright{}…

Precise determination of the171Yb+ ground state Hyperfine separation

We performed a microwave-optical double resonance experiment on the ground state of171Yb+ ions. About 105 particles were confined in a r.f. quadrupole trap for periods of several hours in the presence of He buffer gas. Hyperfine pumping by a pulsed dye laser was followed by microwave transitions, which we observed via changes in the ionic fluorescence intensity. The ground state hyperfine splitting has been determined togD W=12642812124.2±1.4 Hz. The ultimate line width obtained in this experiment was 33 mHz, corresponding to a lineQ of 3.8·1011. The final error ofgD W is mainly determined by the accuracy of the available frequency reference.

Doppler free ?dark resonances? for hyperfine measurements and isotope shifts in Ca+ isotopes in a Paul trap

We have observed “dark resonances” in theA-type level structure, formed by the 4S1/2 ground state, the 4P1/2 excited state and the low lying metastable 3D3/2 state in the Calcium ion, confined in a Paul radio-frequency trap. These Doppler-free and potentially very narrow resonances were used to determine the magnetic dipole hyperfine interaction constant A for the 4P1/2 and 3D3/2 state of43Ca+, giving −142(8) MHz and −48.3(1.6) MHz, respectively. From measurements of the P-D (E1) and S-D (E2) transition wavelength in a mixture of43Ca+ and40Ca+ we determined the isotope shifts of these lines.

Precise determination of the ground state hyperfine structure splitting of43Ca II

We have performed a laser microwave double resonance experiment on43Ca+ ions stored in a Paul ion trap. The ground state hfs splitting has been determined to Δν=3 225 608 286. 4(3) Hz. The value is corrected for small Zeeman, Stark and second order Doppler shifts as well as for light shift effects caused by the laserfields. The uncertainty is mainly determined by the errors of these corrections.

The g-factor of the Electron Bound in Hydrogen-like Ions

The experimental determination of the magnetic moment (g-factor) of the electron bound in hydrogen-like ions represents a clean test of Quantum Electrodynamics, because it is not very sensitive to nuclear structure effects. Experimental data on the g-factor of the bound electron are available only for the hydrogen atom and the 4He+-ion. In this paper we present the first result for the g-factor of hydrogen-like carbon (12C5+). The experimental accuracy is high enough to verify the relativistic contribution to the g-factor on the 10-3 level.

High-resolution microwave spectroscopy on trapped ion clouds

Ion traps are particular usefully devices for precision spectroscopy on ionic ground states in the microwave domain. Although ultimate precision is achieved only with laser-cooled single ions, in many cases the precision obtained using large uncooled clouds of ions is sufficient for many requirements in atomic physics. The stronger signal in this case makes possible experiments on forbidden transitions or on systems with complex spectra and many substates. Recent examples of laser-microwave double resonance spectra on Pb+ and Eu+ are presented along with attempts to laser-cool a large ion cloud in order to reduce uncertainties from the second-order Doppler effect.

Collisional de-excitation of the metastableD-states of Ba+ by He, Ne, N2 and H2

The rate constants 〈σ · υ〉 for collisional de-excitation of the metastable 5D states of Ba+ ions have been determined in an ion trap experiment. TheD-states are selectively populated by pulsed laser excitation of the 6P1/2 or 6P3/2 state and the decay at different background pressures is monitored by the change in fluorescence intensity of the excited ions. From the pressure dependence of the decay constants we calculate the de-excitation rate constants for different collision partners, averaged over the velocity distribution of the trapped ion cloud. For He, Ne, H2 and N2 we obtain in the c.m. energy range of 0.1–0.5 eV: 〈σ·υ〉 (He)=3.0±0.2·10−13cm3/s, 〈σ·υ〉 (Ne)=5.1±0.4·10−13cm3/s, 〈σ·υ〉 (…

Trapping of ions from high energy sources into a radiofrequency ion trap

An attempt is described to confine ions, created externally and accelerated to some energy, in an rf quadrupole trap. 4 keV Ba+ ions were stopped on a Ni foil, placed in an aperture of one trap electrode. The Ba then was evaporated from the heated foil and ionized by electron impact. At background pressure of about 10−5 mbar of various light buffer gases (He, H2, N2), the trap was filled once with 105 ions, at a minimum primary ion number of 1010. The storage time was 10 min. From the data obtained the possibility of spectroseopic experiments on rare isotopes, created with accelerators or nuclear reactors, is discussed.

Measurement of the g Factor of the Bound Electron in Hydrogen-like Oxygen 16O7+

The measurement of the g factor of the electron bound in a hydrogen-like ion is a high- accuracy test of the theory of Quantum Electrodynamics (QED) in strong fields. Here we report on the measurement of the g factor of the bound electron in hydrogen-like oxygen 16O7+. In our experiment a single 16O7+ ion is stored in a Penning trap. Quantum jumps between the two spin states (spin up and spin down) are induced by a microwave field at the spin precession frequency of the bound electron. The g factor of the bound electron is obtained by varying the microwave frequency and counting the number of spin flips. Our experimental value for the g factor of the bound electron is gexp(16O7+) = 2.000 04…

Experimental lifetime of the metastable 5D 3/2 state in Ba+

A discrepancy exists between theoretical and experimental lifetimes of the metastable 5D3/2 state in Ba+. In order to redertermine that lifetime, we probe the population of the metastable 5D3/2 state of a Ba+ ion cloud stored in a Paul ion trap in the presence of He buffer gas as the function of time delay after pulsed laser excitation of this state. The measured decay rates at different buffer gas pressures are extrapolated to zero pressure and we obtain a radiative decay time of 48.0±5.9 s. This is not in agreement with theoretical predictions of about 80 s, but reduces the discrepancy from a previously reportet experimental value of 17.5 s. If the possibility of finestructure mixing to a…

Precision studies in traps: Measurement of fundamental constants and tests of fundamental theories

Experiments on single atomic particles confined in Penning ion traps have contributed significantly to the improvements of fundamental constants and to tests of the theory of Quantum Electrodynamics for free and bound electrons. The most precise value of the fine structure constant as well as the electron mass have been derived from trap experiments. Numerous atomic masses of interest for fundamental questions have been determined with precisions of 10 � 9 or below. Further progress is envisaged in the near future.

Towards electronic g-factor measurements in medium-heavy hydrogen-like and lithium-like ions

Abstract Measurements of the anomalous magnetic moment of the electron bound in hydrogen-like ions with spinless nuclei have proven to be highly sensitive tests of corresponding calculations based on bound-state quantum electrodynamics. Measurements performed on H-like carbon 12C5+ and oxygen 16O7+ together with bound-state QED calculations on the same level of accuracy have achieved sensitivities around 0.25% of the QED bound state contributions to the calculated electronic g-factors of these ions. Currently, a similar experiment on hydrogen-like calcium 40Ca19+, lithium-like calcium 40Ca17+ and other medium-heavy ions is being prepared, which is capable of increasing this sensitivity on t…

Precise ground-state hyperfine splitting inii173

A laser-microwave double-resonance experiment on electrodynamically trapped $^{173}\mathrm{Yb}^{+}$ ions has been performed and a value of \ensuremath{\Delta}${\ensuremath{\nu}}_{\mathrm{h}\mathrm{f}\mathrm{s}=10\phantom{\rule{0ex}{0ex}}491\phantom{\rule{0ex}{0ex}}720239.55}$\ifmmode\pm\else\textpm\fi{}0.09 Hz for the ground-state hyperfine separation has been determined. This value is corrected for small Zeeman and second-order Doppler shifts. Combined with a previous similar measurement on $^{171}\mathrm{Yb}^{+}$ and with the known ${g}_{I}$ values of both isotopes, we obtain a value of -0.004 25(6) for the differential hyperfine anomaly $^{171}\mathrm{\ensuremath{\Delta}}^{173}$.

ElectronicgFactor of Hydrogenlike OxygenO7+16

We present an experimental value for the $g$ factor of the electron bound in hydrogenlike oxygen, which is found to be ${g}_{\mathrm{e}\mathrm{x}\mathrm{p}\mathrm{t}}=2.000\text{ }047\text{ }025\text{ }4\text{ }(15)(44)$. The experiment was performed on a single $^{16}\mathrm{O}^{7+}$ ion stored in a Penning trap. For the first time, the expected line shape of the $g$-factor resonance is calculated which is essential for minimizing the systematic uncertainties. The measurement agrees within $1.1\text{ }\ensuremath{\sigma}$ with the predicted theoretical value ${g}_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{o}\mathrm{r}\mathrm{y}}=2.000\text{ }047\text{ }020\text{ }2\text{ }(6)$. It represents a…

Precision determination of the ground-state hyperfine splitting inBa+137using the ion-storage technique

Precision spectroscopy on trapped atomic ions

Recent examples of lifetime measurements, ground state hyperfine splittings and spectroscopy on minute samples of radioactive ions illustrate the extension of classical methods of spectroscopy to new regions of interest by the use of ion storage techniques. Estimates are given on the sensitivity of the method with respect to be possible investigation of the Bohr-Weisskopf effect in isotopic chains of elements.

Ion storage technique for very long living states: The decay rate of the 5D 3/2 state of Ba II

The metastable 5D 3/2 state of Ba+ is used to demonstrate the possibility of the ion storage technique for the measurement of extremely long lived states. The ions are confined in a r.f. quadrupole trap and excited by a strong pulsed tunable dye laser to the 6P 1/2 state which partially decays into the 5D 3/2 state. Sampling of the time development of the ground state population leads to the determination of the 5D 3/2 decay rate. Using He as a buffer gas at a pressure of about 10−6 mbar to initially store the ions, varying the gas density and extrapolating to zero pressure, we find for the lifetime $$\tau _{D_{3/2} } = 17.5 \pm 4s$$ .

Spin dependence of low energy charge exchange between H 2 + and Na

The difference in charge exchange rate in collisions between spin oriented sodium atoms and H 2 + ions has been measured at an energy of about 1 eV. H 2 + was stored in a Penning trap and polarized by spin exchange with Na beam atoms from a hexapole magnet. The ion loss from the trap due to charge exchange was different as we depolarized the atomic beam. From the data we obtain a ratio of cross sections for singlet and triplet collisionsQ 1/Q 3=1.5±0.2 andQ 3=1.2·10−15 cm2.

Ion traps and their application in spectroscopy

The general behaviour of Paul- and Penning ion traps is briefly described and some emphasis is given to the storage of highly charged ions. In the second part recent examples of laser and microwave spectroscopy on stored ions are given which illustrate the high precision and high sensitivity of these devices. We point out the possible application to laser spectroscopy on highly charged ions.

Measurement of the gj factor of hydrogenic ions: a sensitive test of bound state QED

Thegj factor measurement of hydrogenic ions in the 1s ground state is with an expected accuracy of 10−7 a sensitive test of bound state QED. We expect to determine the deviations from the free electron value, caused by relativistic and radiative corrections, up to the orderα/4π(Zα)2 with an accuracy of 1%. As a first step, light ions like C5+ will be investigated. Later on, heavier hydrogenic ions up to U91+ will be examined using the accelerator facilities at GSI in Darmstadt.

Measurement of the4He-D2 mass difference

A Penning ion trap spectrometer has been used to measure the modified cyclotron frequencies of trapped4He+ and D 2 + ions. The resonances were detected by a time of flight method after ejection of the ions from the trap. We obtain a mass differenceΔm (D2-4He) = 25600331(5)·10−9 amu in acordance with published values but with a reduced uncertainty.

Precise $\sf g_J$ - and $\sf g_I$ -factor measurements of Ba + isotopes

Laser-microwave double and triple resonance experiments were performed on clouds of Ba+ ions confined in a Penning ion trap to induce and detect electronic and nuclear spin flip transitions. Collisions with buffer gas molecules in the trap was used to reduce the lifetime of a long lived metastable state of the ions, in which population trapping might occur, and to cool the ions to the ambient temperature. Loss of ions from the trap by collisions were prevented by coupling the magnetron and reduced cyclotron motions by an additional r.f. field at the sum frequency of the two motions. Electronic Zeeman transitions in 138Ba+ and 135Ba+ were observed at a full width of about 3 kHz at a transiti…

High-precision hyperfine spectroscopy inM1-M1 double-resonance transitions on trappedPb+207

Optical pumping of the ground state of $^{207}\mathrm{Pb}^{+}$ ions, confined in a Paul ion trap on the weak 6${\mathit{P}}_{1/2\mathrm{\ensuremath{-}}}$6${\mathit{P}}_{3/2}$ M1 transition at \ensuremath{\lambda}=710 nm, and consequent magnetic-dipole transitions between the ground-state hyperfine Zeeman levels have resulted in an A factor of 12 968 180 601.61(0.22) Hz and linewidth of 0.5 Hz. The value includes corrections of Zeeman shifts from residual magnetic fields and second-order Doppler shifts in the several-eV-deep trap potential, while the ions were cooled by He buffer gas. Two M1 quanta have been applied simultaneously in a double-resonance experiment.

ADIABATIC COOLING OF IONS IN THE PENNING TRAP

An ion cloud in a Penning trap can be cooled by adiabatic expansion by reducing the trap's magnetic and electric fields. We treat the ion cloud as a classical gas and obtain the relations between the temperature and the trapping fields. This cooling method may be useful in trapping and cooling of antiprotons with the aim of measuring the gravitational accleration of anti-protons and other experiments on heavy ions.

Positronium spectroscopy at a LINAC-based slow positron source

The slow positron facility TEPOS at the Giessen electron LINAC (36 MeV, 120 µA) has been used to produce an intense beam of moderated positrons which is magnetically guided over a distance of 9 m. At a transportation energy of 100 eV about 106 slow e+/s could be extracted out of the magnetic field (0.01 T) and have been electrostatically focussed inside a microwave guide. A small fraction of the positrons form positronium in the excited staten=2. The spontaneous emission of Lyman-α photons (λ=243 nm) from the 2P-states is observed by a photomultiplier. Microwave induced fine-structure transitions 23S1©23P2,1,0 have been observed at 8617(2), 13010(3) and 18494(2) MHz by an increase of the Ly…

Lifetime and collisional depopulation of the metastable 5D 3/2-state of Yb+

The lifetime and collisional depopulation rates of the metastable 5D 3/2 state of Yb+ have been determined in a radiofrequency ion trap by observation of the fluorescence count rate after ion excitation by a short laser pulse. From measurements using He, N2 and H2 as buffer gases between 10−8 and 10−6 mbar pressure and linear extrapolation to zero pressure we obtain a lifetime of τ=52.15±1.00 ms and rate constants ofR(H2)=(1.02±0.10)×10−9 cm3/s andR(N2)=(1.78±0.19)×10−10 cm3/s. The lifetime is in fair agreement with a calculated value of 74 ms.

High-precision mass spectrometer for light ions

The precise knowledge of the atomic masses of light atomic nuclei, e.g. the proton, deuteron, triton and helion, is of great importance for several fundamental tests in physics. However, the latest high-precision measurements of these masses carried out at different mass spectrometers indicate an inconsistency of five standard deviations. To determine the masses of the lightest ions with a relative precision of a few parts per trillion and investigate this mass problem a cryogenic multi-Penning trap setup, LIONTRAP (Light ION TRAP), was constructed. This allows an independent and more precise determination of the relevant atomic masses by measuring the cyclotron frequency of single trapped …

Isotope separation by nonlinear resonances in a Paul trap

Deviations from the ideal quadrupole potential in a Paul ion trap create nonlinear resonances at certain operating points inside the stability diagram, where in the absence of potential pertubations storing times are very long. In the presence of those pertubations, however, the ions are lost from the trap. Since these resonances are mass dependent and the mass resolution is of the order of 100 it can be used to separate isotopes of a given element by choosing suitable trap operating conditions. Experiments on a natural mixture of Eu+ ions of mass 151 and 153 show that in a simple way, by proper choice of the operating point, the ions can be completely separated and laser-induced optical sp…

gFactor of HydrogenlikeSi13+28

We determined the experimental value of the $g$ factor of the electron bound in hydrogenlike $^{28}\mathrm{Si}^{13+}$ by using a single ion confined in a cylindrical Penning trap. From the ratio of the ion's cyclotron frequency and the induced spin flip frequency, we obtain $g=1.995\text{ }348\text{ }958\text{ }7(5)(3)(8)$. It is in excellent agreement with the state-of-the-art theoretical value of 1.995 348 958 0(17), which includes QED contributions up to the two-loop level of the order of $(Z\ensuremath{\alpha}{)}^{2}$ and $(Z\ensuremath{\alpha}{)}^{4}$ and represents a stringent test of bound-state quantum electrodynamics calculations.

Zeeman Spectroscopy in Penning Traps

Abstract Penning traps are the instruments of choice to determine the magnetic moments of long lived or stable charged particles. The virtual absence of collisions with background molecules when working in ultra-high vacuum, the small volume which the trapped particles occupy at low kinetic energies, and the extremely long observation and coherence times allow for very high precision in Zeeman spectroscopy. When applied to singly ionized multielectron atoms the experiments serve for tests of atomic structure calculations. The magnetic moments in few-electron systems such as hydrogen- or lithium-like highly charged ions can be calculated with remarkable precision in the frame of bound-state …

Electro-produced slow positrons

During the last 6 years it has been demonstrated that electro-produced intense beams of slow positrons are possible. High energy electrons from an accelerator generate bremsstrahlung in a thick conversion target of high element number Z. The photons produce electronpositron pairs and a small fraction of the positrons may be moderated to thermal energies. A review is given of the existing slow positron beam lines using this technique. At accelerator energies of 100 MeV total conversion efficiencies of several slow positrons per 106 primary electrons have been obtained, resulting in average intensities of several 109 slow positrons per second or more than 105 slow positrons in pulses having a…